Often when asked if you are in a relationship, by saying you have a "domestic partner", it doesn't define your sexual orientation. So, "counter-gender" domestic partner does, plus it can be used by men or women with the same result.

Marginalized Orientations, Gender identities, And Intersex. it’s meant to be an all inclusive umbrella term for asexuals, homosexuals, multisexuals, trans people, and intersex people. Alternative to LGBTQIAP+
Alternative to MOGII, easier to pronounce.